Topological Character Research Articles

Single monkey-saddle singularity of a Fermi surface and its instabilities

Fermi surfaces can undergo sharp transitions under smooth changes of parameters. Such transitions can have a topological character, as is the case when a higher-order singularity, one that requires cubic or higher-order terms to describe the electronic dispersion near the singularity, develops at the transition. When time-reversal and inversion symmetries are present, odd singularities can only appear in pairs within the Brillouin zone. In this case, the combination of the enhanced density of states that accompanies these singularities and the nesting between the pairs of singularities leads to interaction-driven instabilities. We present examples of single $n=3$ (monkey-saddle) singularities when time-reversal and inversion symmetries are broken. We then turn to the question of what instabilities are possible when the singularities are isolated. For spinful electrons, we find that the inclusion of repulsive interactions destroys any isolated monkey-saddle singularity present in the noninteracting spectrum by developing Stoner or Lifshitz instabilities. In contrast, for spinless electrons and at the mean-field level, we show that an isolated monkey-saddle singularity can be stabilized in the presence of short-range repulsive interactions.

Topology and Dimension Synchronous Optimization of 1T2R Parallel Robots

Parallel robots have attracted much attention from both academia and engineering in last two decades. For development of novel parallel robots, topology and dimensions are brought into sharper focus, which are associated closely and have coupled influence on both motion pattern and performance together. However, currently topology design and dimension design are always performed individually with independent aims, leading to local optimal solutions and difficulties in further modification. Actually, the intrinsic relationship between topology and performance is concerned far from abundant. In this article, a method for topology and dimension synchronous optimization is investigated by employing finite screw theory. Within this approach, two algorithms are formulated to parameterize and deliver topology characters in the same format with dimensions. Topology design and dimension design are converted into a synchronous optimization model with mixed variables and multi-objectives, resulting in global optimal solutions of both optimal topology and dimensions. Topology and dimension synchronous optimization of a kind of 1T2R parallel robots is presented and discussed by comparing with state-of-the-art methods.

A Dual-Inductor-Connected Isolated DC–DC Converter With Direct Current Control and Low Current Harmonics

Renewable energy sources such as fuel cells and photovoltaics (PV) modules are widely installed in recent years. Due to these sources’ characteristics such as low port voltage, current-harmonic-sensitive and weak short-circuit withstanding capability, their interface converters usually require high voltage gains, low high-frequency (HF) current harmonics and short-circuit protection. At present, the existing step-up isolated dc-dc converters are usually combined with two capacitor-connected terminals or one capacitor-connected terminal plus one inductor-connected terminal, failing to obtain the low HF current harmonics and convenient direct current control (DCC) on both ports. Hence, a dual-inductor-connected (DIC) isolated dc-dc converter is proposed in this paper with the inductor connection on both ports. Then, low HF current harmonics and convenient DCC capability can be realized simultaneously through the connected inductors. Meanwhile, the proposed converter can also achieve voltage spike suppression and soft-switching operation without snubber circuits, and its inherent voltage boost function makes it suitable for high voltage-gain applications. Subsequently, the modulation scheme, topology characters and control scheme are elaborated in this paper. The experimental results based on a scale-down laboratory prototype are presented to verify the steady-state and transient-state performance of the proposed converter.

Stress focusing and damage protection in topological Maxwell metamaterials

Advances in the field of topological mechanics have highlighted a number of special mechanical properties of Maxwell lattices, including the ability to focus zero-energy floppy modes and states of self-stress (SSS) at their edges and interfaces. Due to their topological character, these phenomena are protected against perturbations in the lattice geometry and material properties, which makes them robust against the emergence of structural non-idealities, defects, and damage. Recent computational work has shown that the ability of Maxwell lattices to focus stress along prescribed SSS domain walls can be harnessed for the purpose of protecting other regions in the bulk of the lattice from detrimental stress concentration and, potentially, inhibiting the onset of fracture mechanisms at stress hot spots such as holes and cracks. This property provides a powerful, geometry-based tool for the design of lattice configurations that are robust against damage and fracture. In this work, we provide a comprehensive experiment-driven exploration of this idea in the context of realistic structural lattices characterized by non-ideal, finite-thickness hinges. Our experiments document the onset of pronounced domain wall stress focusing, indicating a remarkable robustness of the polarization even in the presence of the dilutive effects of the structural hinges. We also demonstrate that the polarization protects the lattice against potential failure from defected hinges and cracks in the bulk. Finally, we illustrate numerically the superiority of SSS domain walls compared to other trivial forms of reinforcements.

Identification of non-coding RNA related prognosis biomarkers based on ceRNA network in thyroid cancer.

Introduction: Thyroid cancer (THCA) has become a serious malignant tumor worldwide. Identification of non-coding RNA related regulators is very necessary to improve the knowledge of THCA treatment. The aim of this study was to identify novel therapeutic targets and prognosis biomarkers for predicting pathological characteristics and subsequently treating THCA. Methods: We investigated the alterations of miRNAs, mRNAs and lncRNAs in THCA. Functional enrichment and clustering analysis were conducted for these aberrantly expressed RNAs. Multiple interaction networks among miRNAs, mRNAs and lncRNAs were constructed and the functional modules associated with THCA patients' prognosis were identified. Furthermore, we evaluated the prognostic roles of the important miRNAs, mRNAs and lncRNAs in THCA and investigated the regulatory potential of non-coding RNAs on immune cell infiltration. Results: We firstly identified that miR-4709-3p and miR-146b-3p could significantly classify patients into high/low risk groups, which may be potential prognosis biomarkers of THCA. Secondly, we constructed a THCA-related miRNA-mRNA network, which displayed small world network topological characters. Two THCA-related functional modules were identified from the miRNA-mRNA network by MCODE. Results showed that two modules could implicate in known cancer pathways, such as apoptosis and focal adhesion. Thirdly, a THCA-related miRNA-lncRNA network was constructed. A subnetwork of miRNA-lncRNA network showed strong prognosis effect in THCA. Fourthly, we constructed a THCA-related mRNA-lncRNA network and detected several typical lncRNA-miRNA-mRNA crosstalk, such as AC068138, BCL2, miR-21 and miR-146b, which had good prognosis effect in THCA. Immune infiltration results showed that lncRNAs LA16c-329F2, RP11-395N3, RP11-423H2, RP11-399B17 and RP11-1036E20 were high related to neutrophil and dendritic cell infiltration. Discussion: Non-coding RNA-mediated gene regulatory network has the strong regulatory potential in pathological processes of THCA. All these results could help us uncover the non-coding RNA-mediated regulatory mechanism in THCA.

Topologicality of the Whitney topology on function spaces in the ωμ-metric framework

Let X be a Tychonoff space, (Yd) a metric space and C(X,Y) the set of all continuous functions from X to Y. In the classical Whitney topology on C(X,Y) the approximation of functions is done by the means of continuous positive functions from X to the Euclidean real line. It is known that, whenever X is paracompact, the Whitney topology is independent of the metric d, in fact being a topological character. An analogous result holds whenever (Y,d) is replaced by an ωμ-metric space (Y,ρ,G), where ωμ is a regular ordinal number, ρ:Y×Y→G is a distance sharing the usual formal properties with real metrics but valued in an additive totally ordered Abelian group G admitting a strictly decreasing ωμ-sequence converging to zero in the order topology, or, the same, of character ωμ. Precisely, whenever ωμ is an uncountable ordinal and X is paracompact and ωμ-additive, then the Whitney topology on C(X,Y) is independent of the ωμ-metric ρ, in fact being again a topological character. The purpose of this paper is to fill the gap in the case the basic groups are of countable character but eventually non Archimedean. It comes up as very natural the preliminary question: how does a totally ordered Abelian group G look like? The Hahn's Embedding Theorem and the Hahn's Completeness Theorem provide models so making easier the investigation of their order topology in the distinguished two cases of countable character: the basic group G has finitely many Archimedean classes or infinitely many, then countably many, Archimedean classes. In the former, any basic group G with n,n≥2, Archimedean classes can be identified up to a bijective monotone homomorphism with a topological subgroup of Rn, which is a one-dimensional topological group when equipped with the pointwise addition and the lexicographic absolute value metric. In the latter, any basic group G with countably many Archimedean classes can be identified up to a bijective monotone homomorphism with a topological subgroup of Rℵ0, the set of all real sequences, which is a zero-dimensional topological group when equipped with the pointwise addition and the lexicographic absolute value metric. In the former case, we establish the following result including the classic metric one: Let X be paracompact. If(Y,ρ)is a G-metric with G of countable character and with finitely many Archimedean classes, eventually a real metric space, then the Whitney topology onC(X,Y)relative to ρ and G is independent of both ρ and G, in fact being a topological character. And in the latter one, we achieve the general following result: Let X be paracompact and(Y,ρ)a G of countable character and with infinitely many Archimedean classes. Then, the Whitney topology onC(X,Y), when different from the relative uniform topology, is independent of both ρ and G, so agreeing with the classical one, if and only if any real valued positive continuous function on X can be minorized with a positive locally constant function.1

Magnetic Breakdown and Topology in the Kagome Superconductor CsV_{3}Sb_{5} under High Magnetic Field.

The recently discovered layered kagome metals of composition AV_{3}Sb_{5} (A=K, Rb, Cs) exhibit a complex interplay among superconductivity, charge density wave order, topologically nontrivial electronic band structure and geometrical frustration. Here, we probe the electronic band structure underlying these exotic correlated electronic states in CsV_{3}Sb_{5} with quantum oscillation measurements in pulsed fields up to 86T. The high-field data reveal a sequence of magnetic breakdown orbits that allows the construction of a model for the folded Fermi surface of CsV_{3}Sb_{5}. The dominant features are large triangular Fermi surface sheets that cover almost half the folded Brillouin zone. These sheets have not yet been detected in angle resolved photoemission spectroscopy and display pronounced nesting. The Berry phases of the electron orbits have been deduced from Landau level fan diagrams near the quantum limit without the need for extrapolations, thereby unambiguously establishing the nontrivial topological character of several electron bands in this kagome lattice superconductor.

Stability analysis and optimal control in an epidemic model on directed complex networks with nonlinear incidence

In this paper, stability and optimal control for SIS epidemic systems with birth and death in directed complex networks are investigated. A class of epidemic systems are constructed based on SIS models combining with two kinds of topological characters as in-degree and out-degree in directed networks, in which the nonlinear incidence rate is introduced that relevant to network’s topology containing the psychological effect coefficient. The disease-free and the endemic equilibria are derived and the epidemic threshold for our systems is obtained. Then, the local stability about the disease-free and the endemic equilibria are discussed via the corresponding Jacobian matrices and the characteristic equation. In addition, global asymptotical stability about two kinds of equilibria are also considered based on the Lyapunov function and stable analysis method. From the view of Pontryagin Minimum Principle, the optimal control issue about the system is also considered, and the corresponding optimal control systems and optimal control tactics are obtained. Several numerical examples are provided to demonstrate the effectiveness of our main method. Meanwhile, by means of the Forward–Backward Sweep method, optimal control systems are solved in the aspect of numeric and the control aim under the derived strategies is achieved.

First principles insights on the structural, mechanical, dynamical, thermoelectric and thermodynamics properties of novel topological (ScSb) semi-metal

In the present report, we have a detailed investigation of the structural, electronic, mechanical, thermoelectric thermodynamic responses of ScSb with external pressure to full potential Linearized augmented Plane-wave technique (FP-LAPW) and semi-classical Boltzmann transport equation based on density functional theory (DFT). Computed the structure of ScSb compound having ground state energy and dynamically stable. Diverse approximations were employed in electronic properties to account for precise exchange and correlation effects. The dynamically and mechanically stability structure is confirmed by the estimation of phonon and elastic constants such as Bulk modulus, Young’s modulus, Poisson's ratio, and shear anisotropy factor. For the transition of carriers from the valence band to conduction, we calculated the electron localized function (ELF), electron, and hole effective mass. Transports properties calculated against temperature, chemical potential, as well as carriers concentrations by employing the external pressure (0GP, 25 GPa, and 40 Gpa) were studied using the semi-classical equation in Boltzmann theory. Thermodynamics properties were computed with external pressure having the variation of temperature in this material which is investigated across a wide temperature range (200–1200 K). Maximum Power factor, electrical conductivity, and thermal conductivity are determined to be 0.3 × 1010 W/mK2s,3 × 1020 (Ω.m.s)-1, and 2.1 × 1015 W/mKs at 300 K against temperature respectively. Because of its non-trivial topological character, this material has a big power factor, which strongly implies that it can operate as a suitable thermoelectric material in the high-temperature zone.

Non-trivial topological crossover in functionalized AlBi monolayer

The incorporation of spin–orbit coupling and altering the orbital composition close to the Fermi level via functionalization are two essential techniques for exploring topological insulators. We have shown through an ab-initio study that spin–orbit coupling transforms the fluorinated AlBi honeycomb monolayer from a normal insulator to a topological insulator with a large band gap. The combined effects of functionalization and spin–orbit coupling led to a band-inversion in the AlBi honeycomb monolayer. This monolayer has a nontrivial topological character, as confirmed by the reported s/p band inversion in the band structures, the Z2 topological invariant and the clear demonstration of the topological gapless edge states bridging the valence band and conduction band. In addition, it is found that compressing the fluorinated AlBi lattice by about 3 % triggered the topological phase transition, which results in a normal state. The reported nontrivial band gap of 0.36 eV in the fluorinated AlBi monolayer is sufficient to make them a suitable consideration for spintronic devices at room temperature.

Novel classes of fuzzy β-covering-based rough set over two distinct universes

For a deep study of Yang's approach of fuzzy β-covering based rough sets over two distinct universes, we propose novel classes of fuzzy β-covering-based rough set models by introducing the concepts of fuzzy β-minimal and β-maximal descriptions over two distinct universes in this paper. First of all, we propose the definitions of fuzzy β-minimal and β-maximal descriptions over two distinct universes and investigate some of their characteristics. Secondly, we propose four novel types of fuzzy β-neighborhoods over two distinct universes and investigate some of their properties. Meanwhile, we study four types of β-neighborhoods over two distinct universes. Then, we define four types of fuzzy β-covering-based rough set models over two distinct universes by using fuzzy β-neighborhoods. Moreover, some basic properties and topological characters of these novel fuzzy β-covering-based rough approximation operators are investigated. Especially, the relationship among these models are also discussed. Finally, we present some remarks and propositions to clarify the contributions and the relationship between our models and the others.

First-principles studies of electronic properties in a Pt2CdSe3/Pt2HgSe3 Kane-Mele heterobilayer

In this paper, we investigate the electronic band structure and optical conductivity of a ${\mathrm{Pt}}_{2}\mathrm{Cd}{\mathrm{Se}}_{3}/{\mathrm{Pt}}_{2}\mathrm{Hg}{\mathrm{Se}}_{3}$ heterobilayer system composed of two-dimensional jacutingaitelike materials. These layered crystals have shown interesting properties both in bulk as well as in single layers. By using first-principles density functional theory calculations and maximally localized Wannier functions, we show how the electronic and optical properties can be controlled by means of external electric fields. We found that such perturbations can lead to significant changes in the band structure, which are dependent on the orientation of the perpendicular field. In addition, the sign of the Berry curvature around the $K$ and ${K}^{\ensuremath{'}}$ points is dependent on the magnitude and orientation of the external electric field. We also studied the topological character of the structure and found it presents quantum valley Hall states. The sizable band gap in the valley region can be used to manipulate the valley quantum freedom. Moreover, we obtained a strong anisotropy in optical conductivity, where the out-of-plane optical absorption edge is blueshifted with respect to its in-plane counterpart and the application of electric field modifies both intensities and peak positions.

Current-Induced Reversible Split of Elliptically Distorted Skyrmions in Geometrically Confined Fe3 Sn2 Nanotrack.

Skyrmions are swirling spin textures with topological characters promising for future spintronic applications. Skyrmionic devices typically rely on the electrical manipulation of skyrmions with a circular shape. However, manipulating elliptically distorted skyrmions can lead to numerous exotic magneto-electrical functions distinct from those of conventional circular skyrmions, significantly broadening the capability to design innovative spintronic devices. Despite the promising potential, its experimental realization so far remains elusive. In this study, the current-driven dynamics of the elliptically distorted skyrmions in geometrically confined magnet Fe3 Sn2 is experimentally explored. This study finds that the elliptical skyrmions can reversibly split into smaller-sized circular skyrmions at a current density of 3.8× 1010 A m-2 with the current injected along their minor axis. Combined experiments with micromagnetic simulations reveal that this dynamic behavior originates from a delicate interplay of the spin-transfer torque, geometrical confinement, and pinning effect, and strongly depends on the ratio of the major axis to the minor axis of the elliptical skyrmions. The results indicate that the morphology is a new degree of freedom for manipulating the current-driven dynamics of skyrmions, providing a compelling route for the future development of spintronic devices.

Drastic Suppression of CDW (Charge Density Wave) by Pd Addition in TiSe2

TiSe2 is a known Topological semimetal (TSM) having both the semi-metallic and topological characters simultaneously and the Charge density wave (CDW) at below 200K. In the current short article, we study the impact of Pd addition on the CDW character of TiSe2 and the possible induction of superconductivity at low temperatures. Bulk samples of TiSe2 and Pd0.1TiSe2 are synthesized by solid-state reaction route, which is further characterized by powder X-ray diffraction (PXRD) and field emission scanning electron microscopy (FESEM), respectively, for their structural and micro-structural details. The vibrational modes of both samples are being analyzed by Raman spectroscopy, showing the occurrence of both A1g and Eg modes. CDW of pure TiSe2 seen at around 200K in electrical transport measurements, in terms of sharp semi-metallic to metallic transition peak with hysteresis in cooling/warming cycles is not seen in Pd0.1TiSe2, and rather a near metallic transport is seen down to 2K. Although superconductivity is not seen down to 2K, the CDW transition is seemingly completely suppressed in Pd0.1TiSe2. Pd addition in TiSe2 suppresses CDW drastically. Trials are underway to induce superconductivity in Pd-added TiSe2. Density functional theory (DFT) calculations show primary evidence of suppression of CDW by adding Pd in TiSe2 due to an increase in the density of states.

Hourglass charge-three Weyl phonons

The unconventional Weyl point with nonlinear dispersion features higher topological charge $|\mathcal{C}|>1$ and multiple topologically protected Fermi arc states at its boundary. As a novel topological state, it has been attracting widespread attention. However, the unconventional Weyl point with $|\mathcal{C}|=3$ has not yet been reported in realistic materials, even though it has been theoretically proposed for more than a decade. In this work, based on first-principles calculations and theoretical analysis, we predict the existing material $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{LiIO}}_{3}$ as the first realistic example with this unconventional Weyl point. Specifically, in the phonon spectra of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{LiIO}}_{3}$, two Weyl points with $\mathcal{C}=\ensuremath{-}3$, connected by time-reversal symmetry, appear at the neck crossing point of an hourglass-type band, leading to two hourglass charge-3 Weyl phonons. The symmetry protection and the associated novel triple- and sextuple-helicoid surface arc states of the hourglass charge-3 Weyl phonons are revealed. Our results uncover a hidden topological character of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{LiIO}}_{3}$ and also show that the phonon spectra are a great platform for exploring unconventional topological states.

Detailed structural and topological analysis of SnBi2Te4 single crystal

We report herein the successful synthesis of the topological material SnBi2Te4 in single-crystal form. Phase purity and unidirectional growth are evident from X-ray diffraction (XRD) patterns acquired from a powdered sample and a crystal flake. The crystalline morphology has also been visualized by acquiring a field-emission scanning electron microscope (FESEM) image. The crystal has been thoroughly characterized by means of Raman spectroscopy and X-ray photoelectron spectroscopy (XPS) measurements. The topological properties of SnBi2Te4 have been probed through magneto-transport measurements. SnBi2Te4 has been found to exhibit a small but non-saturating magneto-resistance (MR) up to ±12 T. The low-field magnetoconductivity (MC) of SnBi2Te4 at 2 K can be well explained through the Hikami–Larkin–Nagaoka (HLN) formalism, which confirms the presence of a weak anti-localization (WAL) effect in its crystal. Moreover, the non-trivial topological character has been evidenced through first-principles calculations using density functional theory (DFT), with and without spin-orbit coupling (SOC) protocols. A significant change in the bulk electronic band structure is observed upon the inclusion of SOC parameters, signifying topological properties of SnBi2Te4. Its topological non-trivial character has also been verified through calculation of Z2 invariants and the surface states spectrum in the (111) plane.

Direct measurement of topological invariants in photonic superlattices

Since the discovery of topological insulators, topological phases have generated considerable attention across the physics community. The superlattices in particular offer a rich system with several degrees of freedom to explore a variety of topological characteristics and control the localization of states. Albeit their importance, characterizing topological invariants in superlattices consisting of a multi-band structure is challenging beyond the basic case of two-bands as in the Su–Schreifer–Heeger model. Here, we experimentally demonstrate the direct measurement of the topological character of chiral superlattices with broken inversion symmetry. Using a CMOS-compatible nanophotonic chip, we probe the state evolving in the system along the propagation direction using novel nanoscattering structures. We employ a two-waveguide bulk excitation scheme to the superlattice, enabling the identification of topological zero-energy modes through measuring the beam displacement. Our measurements reveal quantized beam displacement corresponding to 0.088 and −0.245, in the cases of trivial and nontrivial photonic superlattices, respectively, showing good agreement with the theoretical values of 0 and −0.25. Our results provide direct identification of the quantized topological numbers in superlattices using a single-shot approach, paving the way for direct measurements of topological invariants in complex photonic structures using tailored excitations with Wannier functions.

Engineering Floquet topological phases using elliptically polarized light

We study a two-dimensional topological system driven out of equilibrium by the application of elliptically polarized light. In particular, we analyze the Bernevig-Hughes-Zhang model when it is perturbed using an elliptically polarized light of frequency $\mathrm{\ensuremath{\Omega}}$ described in general by a vector potential $\mathbf{A}(t)=({A}_{0x}cos(\mathrm{\ensuremath{\Omega}}t),{A}_{0y}cos(\mathrm{\ensuremath{\Omega}}t+{\ensuremath{\phi}}_{0}))$. Even for a fixed value of ${\ensuremath{\phi}}_{0}$, we can change the topological character of the system by changing the $x$ and $y$ amplitudes of the drive. We therefore find a rich topological phase diagram as a function of ${A}_{0x}$, ${A}_{0y}$, and ${\ensuremath{\phi}}_{0}$. In each of these phases, the topological invariant given by the Chern number is consistent with the number of spin-polarized states present at the edges of a nanoribbon.

Imaging scale surface topography of an endemic cyprinid fish, Garra sharq from the Arabian Peninsula: An integrated optical light and scanning electron microscopy approach

AbstractThe optical light microscopy and scanning electron microscopy techniques have proven to play a key and noteworthy role in the advancement of morphological studies in general, and in investigating fish scale morphology in particular. These techniques have illustrated several hidden architectural structures in scales that contribute effectively to fish identification and classification. The scale morphological and topological characters such as type, size, shape, lateral surface, focus position, circuli appearance, radii type, lepidonts, and posterior and anterior margin shapes were obtained using macro‐ and microscopic analysis in six body regions for three size classes of Garra sharq, a cyprinid endemic fish of the Arabian Peninsula. The general scale type in the studied G. sharq species was a basal elasmoid cycloid and a sectioned type. As a protective structure, the scales display several specific characteristics including firm attachment to the fish body, overlapping, and thin structure with a high surface area and high strength. These characteristics improve scale resistance to penetration, increase protection against mechanical injury and microbial infection, enhance scale flexibility, reduce fish weight (reduce friction drag), and increase scale transparency. The scales demonstrate plasticity in focus shape, size, and position in the six fish body parts and fish size groups. The examined scales displayed narrow or wide grooves (radii) in three types including primary, secondary, and tertiary present in all four scale fields (anterior, posterior, and laterals), thus a tetra‐sectioned type that is almost specific to the genus Garra. This characteristic also increases scale flexibility. The rostral margin of scales was characterized by the presence of waved and striate types. The lepidont shape and size varied being blunt, flat, pointed, tiny, sharp, short, and long. Some of these scale characters and their morphologies could be used as an alternative tool for identification, classification, and phylogenetic interpretation among the different freshwater fish species and genera.

Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands

We investigate the existence of acoustic Tamm states at the interface between two one-dimensional (1D) comblike phononic crystals (PnCs) based on slender tubes and discuss their topological or trivial character. The PnCs consist of stubs grafted periodically along a waveguide and the two crystals differ by their geometrical parameters (period and length of the stubs). We use several approaches to discuss the existence of Tamm states and their topology when connecting two half-crystals. First, we derive a necessary and sufficient condition on the existence of interface states based on the analysis of the bulk band structure and the symmetry of the band edge states. This approach is equivalent to an analysis of the Zak phases of the bulk bands in the two crystals. Indeed, a topological interface state should necessarily exist in any common bandgap of the two PnCs for which the lower (upper) band edges have opposite symmetries. A novelty of our structure consists in the fact that the symmetry inversion results from a band closure (flat band) rather than from a gap closure, in contrast to previous works. Then, such interface states are revealed through different physical quantities, namely: (i) the local density of states (LDOS), which exhibits a high localization around the interface; (ii) sharp peaks in the transmission spectra in the common bandgap when two finite crystals are connected together; (iii) the phases of the reflection coefficients at the boundary of each PnC with a waveguide, which have a direct relationship with the Zak phases. In addition, we show that the interface states can transform to bound states in the continuum (BICs). These BICs are induced by the cavity separating both PnCs and they remain robust to any geometrical disorder induced by the stubs and segments around this cavity. Finally, we show the impossibility of interface states between two connected PnCs with different stub lengths and similar periods. The sensitivity of these states to interface perturbations can find many practical applications in PnC sensors.